Independence notions from a general algebraic point of view
by
Kazimierz Glazek
Institute of Mathematics, Technical University of Zielona Gora, Poland

In 1958 E. Marczewski introduced a general notion of independence, which contained as special cases majority of independence notions used in various branches of mathematics. A non-empty set I of the carrier A of an algebra is called M-independent if equality of two term operations f and g of the considered algebra on any finite system of different elements of I implies f=g in A. There are several interesting results on this notion of independence. However the important scheme of M-independence is not enough wide to cover the stochastic independence, the independence in projective spaces and some others. This is why some notions weaker than the M-independence were developed. The notion of independence with respect to family Q of mappings (defined on subsets of A) into A, Q-independence for short, is a common way of defining almost all known notions of independences. There exists an interesting Galois correspondence between families Q of mappings and families of Q-independent sets. In our talk after a brief survey of these topics we will mainly concentrate on a few easily formulated and interesting results.

Date received: June 25, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caiv-27.